def questions1_6():
path_wheel = "../resource/wheele.pgm"
# Question 1.1
img = read_pgm(path_wheel)
(width, height) = img.shape
display_image(img, True)
# Question 1.2
ft2d = fft2(img)
sum = sum_pixels(img)
freqSol = solve_discret_equation_FT(ft2d, sum)
# Question 1.3
spectrum_2D = power_spectrum_2D(ft2d)
display_image(spectrum_2D, vmin=min(spectrum_2D.flatten()), vmax=max(spectrum_2D.flatten()), xlabel='u (frequency)', ylabel='v (frequency)')
# Question 1.4
ft2d_shifted = fftshift(ft2d)
spectrum_shifted_2D = power_spectrum_2D(ft2d_shifted)
img_size = img.shape[0] * img.shape[1]
display_image(spectrum_shifted_2D,
vmin=min(spectrum_shifted_2D.flatten()),
vmax=max(spectrum_shifted_2D.flatten()),
extent=[- height / 2 + 1, height / 2 + 1, - width / 2 + 1, width / 2 + 1])
# Question 1.6
img_computed = ifft2(ft2d)
img_computed = img_computed.astype(int)
display_image(img_computed, True)
def pfft(f, nR = -1): if(nR < 0): nR = int(round(sqrt(2.) * norm(f.shape) + 1)) tf = f if(norm(f.shape) < nR): tf = cpad(f, array([nR, nR])) return rect2polar(ifftshift(fft2(ifftshift(tf))), nR)
def questions1_6():
path_wheel = "../resource/wheele.pgm"
# Question 1.1
img = read_pgm(path_wheel)
(width, height) = img.shape
display_image(img)
# Question 1.2
ft2d = fft2(img)
sum = sum_pixels(img)
freqSol = solve_discret_equation_FT(ft2d, sum)
# Question 1.3
# there is the first version of the answer
# epsilon = np.finfo(float).eps
# axis = np.array(range(0, width * height))
# spectrum = power_spectrum(ft2d)
# display_plot(axis, spectrum,
# xlabel='Fourier domain\'s index (= x + y*width)',
# ylabel='log(modulus(ft(x, y))^2)',
# limits=[0, width * height, min(spectrum), max(spectrum)])
# here what i think is right (another version)
spectrum_2D = power_spectrum_2D(ft2d)
display_image(spectrum_2D,
vmin=min(spectrum_2D.flatten()),
vmax=max(spectrum_2D.flatten()))
# Question 1.4
# there is the first version of the answer
# ft2d_shifted = fftshift(ft2d)
# spectrum_shifted = power_spectrum(ft2d_shifted)
# axis = np.array(range(- width*height / 2 + 1, width * height / 2 + 1))
# display_plot(axis, spectrum_shifted,
# xlabel='Fourier domain\'s index (= x + y*width)',
# ylabel='log(modulus(ft(x, y))^2)',
# limits=[- width * height / 2, width * height / 2 + 2, min(spectrum), max(spectrum)])
# here what i think is right (another version)
ft2d_shifted = fftshift(ft2d)
spectrum_shifted_2D = power_spectrum_2D(ft2d_shifted)
img_size = img.shape[0] * img.shape[1]
display_image(spectrum_shifted_2D,
vmin=min(spectrum_shifted_2D.flatten()),
vmax=max(spectrum_shifted_2D.flatten()),
extent=[
-height / 2 + 1, height / 2 + 1, -width / 2 + 1,
width / 2 + 1
])
# Question 1.6
img_computed = ifft2(ft2d_shifted)
img_computed = img_computed.astype(int)
display_image(img_computed)
def questions1_6():
path_wheel = "../resource/wheele.pgm"
# Question 1.1
img = read_pgm(path_wheel)
(width, height) = img.shape
display_image(img)
# Question 1.2
ft2d = fft2(img)
sum = sum_pixels(img)
freqSol = solve_discret_equation_FT(ft2d, sum)
# Question 1.3
# there is the first version of the answer
# epsilon = np.finfo(float).eps
# axis = np.array(range(0, width * height))
# spectrum = power_spectrum(ft2d)
# display_plot(axis, spectrum,
# xlabel='Fourier domain\'s index (= x + y*width)',
# ylabel='log(modulus(ft(x, y))^2)',
# limits=[0, width * height, min(spectrum), max(spectrum)])
# here what i think is right (another version)
spectrum_2D = power_spectrum_2D(ft2d)
display_image(spectrum_2D, vmin=min(spectrum_2D.flatten()), vmax=max(spectrum_2D.flatten()))
# Question 1.4
# there is the first version of the answer
# ft2d_shifted = fftshift(ft2d)
# spectrum_shifted = power_spectrum(ft2d_shifted)
# axis = np.array(range(- width*height / 2 + 1, width * height / 2 + 1))
# display_plot(axis, spectrum_shifted,
# xlabel='Fourier domain\'s index (= x + y*width)',
# ylabel='log(modulus(ft(x, y))^2)',
# limits=[- width * height / 2, width * height / 2 + 2, min(spectrum), max(spectrum)])
# here what i think is right (another version)
ft2d_shifted = fftshift(ft2d)
spectrum_shifted_2D = power_spectrum_2D(ft2d_shifted)
img_size = img.shape[0] * img.shape[1]
display_image(spectrum_shifted_2D,
vmin=min(spectrum_shifted_2D.flatten()),
vmax=max(spectrum_shifted_2D.flatten()),
extent=[- height / 2 + 1, height / 2 + 1, - width / 2 + 1, width / 2 + 1])
# Question 1.6
img_computed = ifft2(ft2d_shifted)
img_computed = img_computed.astype(int)
display_image(img_computed)
def questions1_6():
path_wheel = "../resource/wheele.pgm"
# Question 1.1
img = read_pgm(path_wheel)
(width, height) = img.shape
# display_image(img, True)
# Question 1.2
ft2d = fft2(img)
sum = sum_pixels(img)
freqSol = solve_discret_equation_FT(ft2d, sum)
# Question 1.3
spectrum_2D = power_spectrum_2D(ft2d)
# display_image(
# spectrum_2D,
# vmin = min(spectrum_2D.flatten()),
# vmax = max(spectrum_2D.flatten()),
# xlabel= 'u (frequency parameter of the Fourier transform)',
# ylabel= 'v (frequency parameter of the Fourier transform)',
# title = 'Spectrum of the wheele picture')
# Question 1.4
ft2d_shifted = fftshift(ft2d)
spectrum_shifted_2D = power_spectrum_2D(ft2d_shifted)
img_size = img.shape[0] * img.shape[1]
display_image(spectrum_shifted_2D,
vmin=min(spectrum_shifted_2D.flatten()),
vmax=max(spectrum_shifted_2D.flatten()),
extent=[
-height / 2 + 1, height / 2 + 1, -width / 2 + 1,
width / 2 + 1
],
xlabel='u (frequency parameter of the Fourier transform)',
ylabel='v (frequency parameter of the Fourier transform)',
title='Spectrum of the wheele picture (shifted)')
# Question 1.6
img_computed = ifft2(ft2d)
img_computed = img_computed.astype(int)
# display_image(img_computed, True)
if __name__ == "__main__":
# I moved questions 1.1-1.6 to separate function to work on the rest of questions
questions1_6()
path_chess = "../resource/damierHV.pgm"
# Question 1.7
img = read_pgm(path_chess)
(width, height) = img.shape
# display_image(img, True)
# Question 1.8
ft2d = fft2(img)
ft2d_shifted = fftshift(ft2d)
spectrum_shifted_2D = power_spectrum_2D(ft2d_shifted)
img_size = img.shape[0] * img.shape[1]
# display_image(spectrum_shifted_2D,
# vmin=min(spectrum_shifted_2D.flatten()),
# vmax=max(spectrum_shifted_2D.flatten()),
# extent=[- height / 2 + 1, height / 2 + 1, - width / 2 + 1, width / 2 + 1],
# xlabel= 'u (frequency parameter of the Fourier transform)',
# ylabel= 'v (frequency parameter of the Fourier transform)',
# title = 'Spectrum of the chess board picture')
# print("min = " + str(min(spectrum_shifted_2D.flatten())) + ", max = " + str(max(spectrum_shifted_2D.flatten())))
# from here i don't really understand WTF is going on
img_computed = img_computed.astype(int)
display_image(img_computed, True)
if __name__ == "__main__":
# I moved questions 1.1-1.6 to separate function to work on the rest of questions
questions1_6()
path_chess = "../resource/damierHV.pgm"
# Question 1.7
img = read_pgm(path_chess)
(width, height) = img.shape
display_image(img, True)
# Question 1.8
ft2d = fft2(img)
ft2d_shifted = fftshift(ft2d)
spectrum_shifted_2D = power_spectrum_2D(ft2d_shifted)
img_size = img.shape[0] * img.shape[1]
display_image(spectrum_shifted_2D,
vmin=min(spectrum_shifted_2D.flatten()),
vmax=max(spectrum_shifted_2D.flatten()),
extent=[- height / 2 + 1, height / 2 + 1, - width / 2 + 1, width / 2 + 1])
# print("min = " + str(min(spectrum_shifted_2D.flatten())) + ", max = " + str(max(spectrum_shifted_2D.flatten())))
# from here i don't really understand WTF is going on
# Question 1.9
spectrum_x_0 = power_spectrum_2D(ft2d_shifted, fx=0)
spectrum_x_26 = power_spectrum_2D(ft2d_shifted, fx=-26)
